Servo controller method and apparatus for high tracks per inch hard disk drives using a delay accomodating state estimator

ABSTRACT

The invention applies to servo controllers for at least the voice coil motor of a hard disk drive. Today, many control algorithms require 80 to 90 percent of the sampling period to complete their calculation of the next control, making computation time delay no longer negligible. The invention accommodates the transport delay, such as computation time delay, into the state estimator and into the whole control system. Experimental results using a commercial hard drive, as well as simulation results, show that the invention&#39;s method effectively improves the hard disk drive control system stability by increasing the phase margin and gain margin. The invention includes the method of operating the servo-controller, as well as the apparatus implementing that method. The invention also includes hard disk drives containing servo-controllers implementing the method, and program systems residing in accessibly coupled memory to a computer within the servo controller implementing the method.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/903,720 filed Jul. 29, 2004.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to the servo controller operating at least thevoice coil of a voice coil actuator in a hard disk drive.

2. Background Information

Modem hard disk drives include a servo controller driving at least avoice coil actuator to position a read-write head near a track on arotating disk surface. The read-write head communicates with the servocontroller, providing feedback, which is used in controlling theread-write head's positioning near the track. The read-write head isembedded in a slider, which floats, on a thin air bearing, a very shortdistance above the rotating disk surface.

A voice coil actuator typically includes a voice coil, which swings atleast one actuator arm in response to the servo controller. Eachactuator arm includes at least one head gimbal assembly typicallycontaining a read-write head embedded in a slider. The head gimbalassembly couples through a load beam to the actuator arm in the voicecoil actuator. The read-write heads mount on head gimbal assemblies,which float on the thin air bearing off the hard disk drive surface whenin operation. The air bearing is formed by the rotating disk surface andthe slider attached to the head gimbal assembly.

A hard disk drive may have one or more disks. Each of the disks may haveup to two disk surfaces in use. Each disk surface in use has anassociated slider, with the necessary actuator arm. One actuator armtypically supports one or two sliders. Hard disk drives typically haveonly one voice coil actuator.

Often there is one slider for a given hard disk drive surface. There areusually multiple heads in a single hard disk drive, but for economicreasons, usually only one voice coil actuator.

Voice coil actuators are further composed of a fixed magnet whichinteracts with a time varying electromagnetic field induced by a voicecoil. This provides a lever action via an actuator axis. The leveraction acts to move the actuator arm(s), positioning the head gimbalassembly(ies) over specific tracks with speed and accuracy. Actuatorsoften include the voice coil, the actuator axis, the actuator arms andthe head gimbal assemblies. An actuator may have as few as one actuatorarm. A single actuator arm may connect with two head gimbal assemblies,each with at least one head slider.

Typically, a slider is rigidly attached to a head suspension to make ahead gimbal assembly. The attachment of the slider is through a flexure,which provides an electrical interconnection between the read-write headin the slider and the disk controller.

The hard disk drive controller controls the voice coil to position theread-write head over a track above a rotating disk surface. In a typicalhard disk drive control system, the state-space controller/observer (orestimator) design is frequently used. This approach has advantages, suchas effective filtering of position and velocity, use of an estimationerror to handle servo defects, etc. A state space controller isgenerally regarded as a control mechanism exerting a control, based uponfeedback and an internal state. The feedback often includes a PositionError Signal (PES).

These state-space or discrete-time state estimators are typicallyimplemented in one of two forms. One form is the so-called predictionestimator that estimates the state variable based on the plant outputand control of the previous sampling period. The other form is calledthe current estimator, which comes from the use of the current timemeasurement to estimate the state variables. The plant as used hereinrefers to the voice coil actuator interacting with the rotating disksurface(s) to create the measured current read-write head position Ycur.

Prediction estimator equations have a more direct relationship with theinternal dynamics of the hard disk drive. The prediction estimatorequations are a discrete time step form of a continuous-time stateobserver model. However, the current estimator equations can be derivedby means of a discrete Kalman filter formalism with a predeterminedknowledge of the current measurements. Today, the current estimator isthe predominant hard disk drive servo control model. This is due to thebelief that its estimates are more reliable for small computationaldelays.

As the track density (measured tracks-per-inch, or TPI) of hard diskdrives increases, the requirement for servo positioning accuracyincreases. This requirement forces the sampling rate to also beincreased. At the same time, more sophisticated control algorithms needto be used to minimize the Track Mis-Registration (TMR) as the trackdensity, TPI, increases.

The inventors have discovered that a number of previously held andunquestioned assumptions regarding at least computational delays are nolonger true. The computation time delay is no longer negligibly small.It needs to be accounted for in the design of the servo controller.

A portion of each hard disk drive's accessible data is reserved toidentify the read-write head location. Increasing the sampling rateabove certain thresholds requires reducing the data available for use bya computer accessing the hard disk drive, which reduces its marketvalue. This market constraint significantly limits the samplingfrequency, while at the same time, the TPI continues to grow.

Control systems need to account for these new and previouslyinsignificant realities in hard disk drives, without unnecessarilyincreasing the data overhead to support increased sampling rates.

BRIEF SUMMARY OF THE INVENTION

The invention applies to servo controllers in hard disk drives, whichcontrol at least a voice coil motor positioning a read-write head toaccess a track on a rotating disk surface.

Today's hard disk drive control systems tend to use A/D sampling in therange of 24K samples per second. Contemporary control algorithms canrequire 80 to 90 percent of the sampling period to complete theircalculation of the next control. For these reasons, the computation timedelay is no longer negligibly small.

The invention includes simple, yet systematic techniques, accounting forthe transport delay, which may include a computation time delay, in thestate estimator and the whole control system.

The transport delay is defined herein as the time lag between theidealized time of hard disk drive plant output (position) sampling andthe time at which the corresponding control becomes effective at theinput of our design-oriented plant model. The transport delay mayinclude the analogue-to-digital (and vice-versa) conversion time,demodulation time, computational time, time-lag due to finite bandwidthpower amplification, etc..

Experimental results using a commercial hard drive, as well assimulation results, show that the inventive method effectively improvesthe hard disk drive control system stability by increasing the phasemargin and the gain margin.

The invention accounts for the transport delay, and may provideincreased reliability and improved performance today, and as the TPIcontinues to increase.

The invention includes the method of operating the servo-controller, aswell as the apparatus implementing that method. The invention alsoincludes hard disk drives containing servo-controllers implementing themethod, and program systems residing in accessibly coupled memory to acomputer within the servo controller implementing the method.

These and other advantages of the present invention will become apparentupon reading the following detailed descriptions and studying thevarious figures of the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and features of the present invention, which are believed tobe novel, are set forth with particularity in the appended claims. Thepresent invention, both as to its organization and manner of operation,together with further objects and advantages, may best be understood byreference to the following description, taken in connection with theaccompanying drawings, in which:

FIGS. 1A and 1B show a contemporary hard disk drive in which theinvention can provide advantage;

FIG. 2A shows the suspended head gimbal assembly of FIGS. 1A and 1B;

FIG. 2B shows the relationship between the principal axis of an actuatorarm with respect to a radial vector from the center of rotation ofspindle hub for the hard disk drive of FIGS. 1A and 1B;

FIG. 2C shows a typical flexure employed in the head gimbal assembly ofFIG. 2A;

FIG. 2D shows a detail of the flexure of FIG. 2C;

FIG. 2E shows a simplified schematic of a hard disk drive controllerused to control the hard disk drive of FIGS. 1A and 1B;

FIG. 3A shows a simplified timing diagram of discrete-time controllersof FIG. 2E with computational time delay;

FIG. 3B shows a detail flowchart of the program system of FIG. 2E;

FIG. 4A shows the bode plots of simulating an ideal plant with standardcontrol as found in the prior art;

FIG. 4B shows the bode plots of simulating the delay plant with standardcontrol as found in the prior art;

FIG. 5A shows the bode plots of simulating the delay plant with delaymodel estimator;

FIG. 5B shows the bode plots of simulating a state-space controllerdesigned according to a delay-present actuator with the invention'sdelay-accommodating estimator (DAE);

FIG. 6A shows a comparison of the open-loop transfer functions as bodeplots experimentally derived for a prior art design and the DAE basedcontroller design;

FIG. 6B shows a comparison of the error sensitivity functionsexperimentally derived for the prior art design and the DAE basedcontroller design;

FIG. 7A shows a detail flowchart of FIG. 3B; and

FIG. 7B shows a detail flowchart of FIG. 7A.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description is provided to enable any person skilled inthe art to make and use the invention and sets forth the best modespresently contemplated by the inventors for carrying out the invention.Various modifications, however, will remain readily apparent to thoseskilled in the art, since the generic principles of the presentinvention have been defined herein.

Today's hard disk drive control systems tend to use A/D sampling in therange of 24K samples per second. Contemporary control algorithms canrequire 80 to 90 percent of the sampling period to complete theircalculation of the next control. For these reasons, the computation timedelay is no longer negligibly small.

FIG. 1A shows a contemporary hard disk drive 10 including the actuator30 with the voice coil 32, the actuator axis 40, the actuator arms 50-56and with the head gimbal assembly 60 placed among the disks. Theinvention can provide advantage to this hard disk drive.

FIG. 1B shows the hard disk drive 10 of FIG. 1A, with the fixed magnetic20 interacting with the actuator assembly 30 with the disks removed. Theactuator assembly 30 includes the voice coil 32, the actuator axis 40,the actuator arms 50-56 and the head gimbal assembly 60-66.

FIG. 2A shows the suspended head gimbal assembly 60 of FIGS. 1A and 1B,containing a slider 100, which includes the read-write head 200.

The hard disk drive 10 often uses at least the voice coil actuatorsincluding 20-66 of FIGS. 1A to 2A, to position their read-write headsover specific tracks.

The read-write heads 200 are embedded in the sliders 100, as shown inFIG. 2A. Each slider 100 mounts on a head gimbal assembly 60, whichfloats a small distance off the rotating disk surface 12, shown in FIGS.1A to 1B, on an air bearing. The rotating disk surface 12 interactingwith the slider 100 forms the air bearing.

Voice coil actuators are further composed of a fixed magnet actuator 20,interacting with a time varying electromagnetic field induced by thevoice coil 32, to provide a lever action via the actuator axis 40. Thelever action acts to move the actuator arms 50-56 positioning the headgimbal assemblies 60-66 over specific tracks with speed and accuracy.Actuator assemblies 30 typically include the voice coil 32, the actuatoraxis 40, at least one of the actuator arms 50-56 and their head gimbalassemblies 60-66. An actuator assembly 30 may have as few as oneactuator arm 50. A single actuator arm 52 may connect with two headgimbal assemblies 62 and 64, each with at least one head slider 100.

Head gimbal assemblies 60-66 are typically made by rigidly attaching aslider 100 to a head suspension, with a flexure providing electricalinterconnection between the read-write head in the slider and the diskcontroller circuitry. The head suspension is the visible mechanicalinfrastructure of 60-66 in FIGS. 1A to 2A.

FIG. 2B shows the relationship between the principal axis 110 of anactuator arm 50 with respect to a radial vector 112 from the center ofrotation of spindle hub 80. The actuator arm assembly 50-60-100, pivotsabout the actuator axis 40, changing the angular relationship betweenthe radial vector 112 and the actuator principal axis 110. Typically, anactuator arm assembly 50-60-100 rotates through various angularrelationships.

The farthest inside position of the actuator assembly is the InsidePosition denoted herein as ID. The position where radial vector 112approximately makes a right angle with the principal axis 110 is theMiddle Position, denoted herein as MD. The farthest out position wherethe read-write head 100 accesses the disk surface 12 is the OutsidePosition, denoted herein as OD.

As shown in FIG. 2B, the X axis is preferably situated along theprincipal axis 110 of the actuator arm. The Y axis preferably intersectsthe X axis at essentially the actuator pivot 40. When the actuatorpositions the slider 100 so that the read-write head 200 is at MD, theradial vector 112 is essentially parallel to the Y axis. Physical track18 is shown near MD, but physical tracks exist from ID to OD, throughoutthe disk surface 12.

FIGS. 2C and 2D show flexures including a suspension trace 210 providingan electrical interconnection between the read-write head 200 and theanalog interface of a hard disk drive.

FIG. 2E shows a simplified schematic of a hard disk drive controller1000 used to control an assembled hard disk drive 10.

Hard disk drive controller 1000 controls an analog read-write interface220 communicating the resistivity found in the spin valve within theread-write head 200.

The analog read-write interface 220 frequently includes a channelinterface 222 communicating with a pre-amplifier 224. The channelinterface 222 receives commands, from the embedded disk controller 1000,setting at least the read_bias and the write_bias.

Various hard disk drive analog read-write interfaces 220 may employeither a read current bias or a read voltage bias. By way of example,the resistance of the read-write head is determined by measuring thevoltage drop (V_rd) across the read differential signal pair (r+ and r−)based upon the read bias current setting (read_bias), using Ohm's Law.

In FIG. 2E, the channel interface 222 also provides a Position ErrorSignal (PES) to at least the servo controller 240. The servo controller240 uses the PES signal to control at least the voice coil 32. The goalis to keep the read-write head 200 close enough to a physical track 18of FIG. 2B, to support the read-write head 200 communicatively accessingthe physical track 18.

In FIG. 2E, the servo controller 240 provides a control feedback loop.The control feedback loop may use any combination of the following. Alow pass filter, a high pass filter, a band-pass filter, an operationalamplifier, an amplifier, a current source, a delay element, a voltagesource, a comparator, a finite state machine, a digital signalprocessor, an analog-to-digital converter, a channel interface circuit,and a digital-to-analog converter.

In FIG. 2E, the DSP 2000 controls 2032 a DAC 2030, based upon a controlvariable U 2302 and a current read-write head position Ycur 2300, whichis measured. The DAC 2030 often contains a digital-to-analog converterdriving either a current source or a voltage source. The output of theDAC 2030 is presented 2042 to a filter 2040. The filter 2040 may includeat least one of the following: a low pass filter, a high pass filter,and/or a band-pass filter. The filter 2040 output 2052 is presented to apower amplifier 2050, which drives 244 the voice coil 32.

The invention includes a method of designing and operating aservo-controller 240.

In the past, a state-space controller/observer (or estimator) design wasoften used for the servo-controller 240. A state space controller isgenerally regarded as a control mechanism exerting a control 244, basedupon feedback and an internal state, often held in memory 2020. Thefeedback is shown in FIG. 2E as 242 and/or PES. The internal stateincludes a control variable U 2303 residing in memory 2020.

These state-space or discrete-time state estimators can be implementedin two forms. One form is the so-called prediction estimator thatestimates the state variable based on the plant output and the controlof the previous sampling period. The other form is called the currentestimator, which uses the current time step measurement to estimate thestate variables. The plant as used herein refers to the voice coilactuator interacting with the rotating disk surface(s) to create thecurrent read-write head position Ycur 2300, as shown in FIGS. 1A to 2E.

Prediction estimator equations have a more direct relationship with theinternal dynamics of the hard disk drive. The prediction estimatorequations are a discrete time step form of a continuous-time stateobserver model. However, the current estimator equations can be derivedby means of a discrete Kalman filter formalism with a predeterminedknowledge of the current measurements. Today, the current estimator isthe predominant hard disk drive servo control model. Its estimates areregarded as more reliable for small computational delays.

The prior art includes several proposed techniques to incorporate thecomputational delay into control systems design. One of the mostcommonly adopted techniques is to use the input-delayed model in thestate estimator's prediction stage as discussed in “Digital Control ofDynamic Systems” third edition, by Franklin, et. al. referred tohereafter as Franklin. While the state estimation is more reliable, itcannot compensate for the delay in the state feedback law.

An outgrowth of this technique modifies the feedback law to include theone-sample delayed control signal as in the following references. K. S.Rattan, “Compensating for Computational Delay in Digital Equivalent ofContinuous Control Systems,” IEEE Trans. on Automatic Control, Vol.34,No.8, 1989, referred hereafter as Rattan. And T. Mita, “Optimal DigitalFeedback Control Systems Counting Computation Time of Control Laws,”IEEE Trans. on Automatic Control, Vol.AC-30, No.6, 1985 referred tohereafter as Mita.

Rattan develops a similar method for a discrete-equivalent design.However, these methods complicate the servo design, with the potentialto increase computational delay, as well as to complicate and thereforeslow the development process.

Traditionally, delay is modeled as follows. From the continuous-timepoint of view, the presence of computation delay T, is modeled using anideal transport delay element e^(−T) ^(d) ^(s). In most of theliterature, this delay element commonly precedes the voice-coil motor(VCM) dynamics. This leads to the following input-delayed state-spacerepresentation of the plant dynamics for the voice coil actuator 30interacting with the rotating disk surfaces 12:{dot over (x)}(t)=A _(p) x(t)+B _(p) u(t−T _(d)) y(t)=C _(p) x(t)   (1)

Here (A_(p), B_(p), C_(p)) are the system matrices of the actual headpositioning system dynamics for the hard disk drive. The state vector isx(t). The symbol u(t) is the control input such as the Voice Coil Magnet(VCM) current applied to the voice coil 32 shown in FIGS. 1A, 1B and 2E.y(t) is the output, which is the head position shown in FIG. 2B. The“dot” represents the first time derivative of the state vector x(t).

(A_(p), B_(p), C_(p)) usually are not exactly known and are often ofvery high dimension. For actual control design, a practical model(denoted e.g. Ae, Be,Ce) will be used that is of smaller order—usually3—and contains position, velocity, and unknown bias force. The flexurecable 210 shown in FIGS. 2C and 2D is the predominant source of unknownbias force.

Franklin documents the most popular approach accounting for input delay,which is the input-delay model. The time instant at which the headposition is sampled is believed to coincide with the discrete-time indexof the sampled system. This is the justification for subtracting thedelay T_(d) from the control signal u(t).

The discrete version of the input-delayed plant model in (1) is found inFranklin:x[k+1]=A _(e) x[k]+B _(e0) u[k]+B _(e1) u[k−1]y[k]=C _(e) x[k].   (2)

The derivation of (2) can be understood with reference to FIG. 3A. Here,(A_(e),B_(e),C_(e)) represent the system matrices of the plant model forcontrol design, which may possibly contain some augmented states forbias prediction. Use of this delay-present plant equation (2) in thecurrent estimator formulation yields:{circumflex over (x)}[k]={overscore (x)}[k]+L(y[k]−C _(e) {overscore(x)}[ k]), {overscore (x)}[k+1]=A _(e) x[k]+B _(e0) u[k]+B _(e1) u[k−1].  (3)

As the track density (TPI) of hard disk drives increases, therequirement for servo positioning accuracy becomes ever higher. Thisrequirement forces the sampling rate to be increased. At the same time,more sophisticated control algorithms need to be used to minimize theTrack Mis-Registration (TMR) as the track density, TPI, increases. Forthese reasons, the computation time delay is no longer negligibly small.

A portion of each hard disk drive's accessible data is reserved toidentify the read-write head location. Increasing the sampling rateabove certain thresholds requires reducing the data available for use bya computer accessing the hard disk drive, which reduces the market valueof the hard disk drive. This market constraint significantly limits thesampling frequency, while at the same time, the TPI continues to grow.

Today's hard disk drive control systems tend to use A/D sampling in therange of 24K samples per second. Contemporary control algorithms canrequire 80 to 90 percent of the sampling period to complete theircalculation of the next control. For these reasons, the computation timedelay is no longer negligibly small.

The invention accounts for transport delays, such as computation timedelay, in the state estimator and in the whole control system.

The transport delay is defined herein as the time lag between theidealized time of the hard disk drive plant output (position) samplingand the time at which the corresponding control becomes effective at theinput of the plant model. The transport delay may include, but is notlimited to, at least one of the following: the analogue-to-digital (andvice-versa) conversion time, the demodulation time, the computationaltime, and a time-lag due to finite bandwidth power amplification.

FIG. 3A shows a simplified timing diagram of the discrete-timecontrollers 240 of FIG. 2E including the computational time delay.

In FIG. 3A, the continuous position 300 of the read-write head 200 overthe rotating surface 12 shown in FIGS. 2A-2B is measure at times U[k−1],U[k], and U[k+1], which are spaced Ts apart in time. Td represents thedelay between sampling the read-write head position y[k] and thediscrete time assertion 244 of the control variable U[k].

Some of the following figures show flowcharts of at least one method ofthe invention, possessing arrows with reference numbers. These arrowswill signify of flow of control, and sometimes data. These controland/or data flows support implementations including, but not limited tothe following. At least one program operation or program threadexecuting upon a computer. Inferential links in an inferential engine.State transitions in a finite state machine. And dominant learnedresponses within a neural network.

The operation of starting a flowchart refers to at least one of thefollowing. Entering a subroutine in a macro instruction sequence in acomputer. Entering into a deeper node of an inferential graph. Directinga state transition in a finite state machine, possibly while pushing areturn state. And triggering a collection of neurons in a neuralnetwork.

The operation of termination in a flowchart refers to at least one ormore of the following. The completion of those operations, which mayresult in a subroutine return. Traversal of a higher node in aninferential graph. Popping of a previously stored state in a finitestate machine. Return to dormancy of the firing neurons of the neuralnetwork.

A computer as used herein will include, but is not limited to aninstruction processor. The instruction processor includes at least oneinstruction processing element and at least one data processing element,each data processing element controlled by at least one instructionprocessing element.

A Digital Signal Processor (DSP) will refer to at least one computerand/or at least one finite state machine.

FIG. 3B shows a detail flowchart of program system 2100 of FIG. 2Edirecting the DSP 2000 to use a control variable U to control the voicecoil actuator including 20-66 in the hard disk drive 10. The controldrives the circuit, including 2032-2030-2042-2040-2052-2050-244 of FIG.2E, which drives the voice coil 32. The voice coil 32 interacts with thefixed magnet 20 to leverage the actuator assembly 30 which thenpositions the read-write head 200 over the track 18 on the rotating disksurface 12 of FIG. 2B.

Operation 2112 controls the voice coil actuator by a control variable U2302 based upon a measured read-write head position Ycur 2300.

Operation 2122 seeks a first track located at a first head position byusing operation 2112 to control the voice coil actuator. Operation 2112controls the voice coil actuator to alter the measured read-write headposition Ycur 2300 to the first head position.

Operation 2132 follows the first track located at the first headposition by using operation 2112. Operation 2112 controls the voice coilactuator to maintain the measured read-write head position Ycur 2300close to the first head position based upon the control variable U 2302.

In FIG. 2E and 3B, control variable U 2302 numerically represents theelectrical power exerted by the power amplifier 2050 presented 244 tothe voice coil 32. As used herein, numerical representations may includeany combination of fixed point and floating numerical formats andarithmetic operations. The voice coil 32 in turn induces anelectromagnetic field actuating a mechanical force upon the actuator arm50 with respect to the fixed magnet 20. U 2302 may be a numericrepresentation of current. The current required to seek a physical trackis often up to 700 milliAmp (mA). The current required to follow aphysical track is often less than 20 mA. The invention also includes U2302 numerically representing voltage.

In FIGS. 2E and 3B, the Ycur 2300 represents the measured read-writehead position.

The invention collectively makes use of Ybar 2310, Xhat 2320, Xbar 2330,K 2340, L 2350, Ae 2360, Be 2370, Ced 2380, and Ded 2390, in a fashionwhich speaks specifically to the inventive matter. These elements, andtheir relationship with Ycur 2300 and U 2302, will first be discussed interms of the control system equations, and then discussed as a method ofoperation as part of the discussion of FIG. 7.

Returning to the issue of modeling delay. The output of the plant modelmay incorporate transport delay with the hard disk drive 10 as follows:{dot over (x)}(t)=A_(p) x(t)+B_(p) u(t) y(t)=C_(p) x(t−T _(d))   (4)

This formulation identifies the discrete-time index of the discretizedsystem with the instant at which the computed control signal becomeseffective to the plant.

The first equation of (4), is known as the state evolution equation.This equation is delay-free in this output-delay formulation. Thisproperty serves as the basis of the invention's Delay-AccommodatingEstimator (DAE).

Two types of estimators can be based on the two delay-present modelrepresentations presented.

Type I: Conventionally, the control input is generated in the same wayas used in a usual state/observer framework, without delayconsideration. That is, for a state regulator with regulator gain K,u[k]=−K{circumflex over (x)}[k].   (5)

This controller cannot prevent the one-sample-delayed state {overscore(x)}[k] from affecting the closed-loop system (see the state predictionequation in (3)). This may result in degradation of the stabilitymargin.

A controller of the following form may act as a partial compensation tothis problem:u[k]=−{circumflex over (k)}{circumflex over (x)}[k]−k ₁ u[k−1]  (6)where {circumflex over (K)} ε R^(1×n) and k₁ ε R are controller gains tobe determined shortly. R refers to the real numbers, R^(n) refers to ann dimensional vector space over R, and R^(m*n) refers to an m*ndimensional vector space over R. In view of (3), the closed-loop systemcan be rendered to behave as the ideal one without transport delay,provided thatB _(e0) u[k]+B _(e1) u[k−1]=−B _(e) K{circumflex over (x)}[k]  (7)for each k. For any choice of gain pair ({circumflex over(K)},{circumflex over (k)}₁) in (6), it is generally impossible tosatisfy (7) for each k. Nonetheless, (7) can still be approximated in aminimum-norm sense by choosing{circumflex over (K)}=B _(e0) ⁺ B _(e) K, {circumflex over (k/)}=B _(e0)⁺ B _(e1) u[k−1]  (8)where B⁺is the left pseudo-inverse of a matrix B defined, by B⁺

(B^(T)B)⁻¹B^(T), where B has full column rank. A more general formulainvolving the singular value decomposition of B can also be used, whichdoes not require B to have full column rank.

Besides the design method discussed above, an LQR formulation can beused for determining the controller gains. This was done in S.Weerasooriya and D. T. Phan, “Discrete-Time LQG/LTR Design and Modelingof a Hard disk drive Actuator Tracking Servo System,” IEEE Trans.Industrial Electronics, Vol.42, No.3, 1995, referred to hereafter asWeersooriya.

Type II. This invention's method, called “Delay-Accommodating Estimator”(DAE) herein, is based on the output-delay model given in (4). Thisapproach uses the following discrete-time variable definitions:x[k]x(kT _(s)), u[k]u(kT _(s)), y[k]C _(e) x[kT _(s) −T _(d)]  (9)

The state variable's time index will be assumed to agree with that ofthe control signal (see FIG. 3A). To obtain the discrete version of (4),also define x_(m)[k]

x(kT_(s)−T_(d)). Then $\begin{matrix}\begin{matrix}{{x\lbrack k\rbrack} = {{e^{T_{d}A}{x_{m}\lbrack k\rbrack}} + {\int_{{kT}_{s} - T_{d}}^{{kT}_{s}}{e^{A{({{kT}_{s} - \tau})}}B_{e}\quad{\mathbb{d}\tau}\quad{u\left\lbrack {k - 1} \right\rbrack}}}}} \\{= {{e^{T_{d}A}{x_{m}\lbrack k\rbrack}} + {\int_{0}^{T_{d}}{e^{\lambda\quad A_{e}}B_{e}\quad{\mathbb{d}\lambda}\quad{u\left\lbrack {k - 1} \right\rbrack}}}}}\end{matrix} & (10)\end{matrix}$where x follows the delay-free state evolution equation:x[k+1]=A _(e) x[k]+B _(e) u[k]  (11)

Now, the following output equation is obtained by using (10):y[k]=C _(ed) x[k]+D _(ed) u[k−1]  (12)where the matrices are defined byC _(ed) C _(e) e ^(−T) _(d) ^(A) _(e) , D _(ed) −C _(e)e^(−T) _(d) ^(A)_(e) ∫₀ ^(t) _(d) e ^(iA) _(e/) B _(e) dλ  (13)

Applying the current state estimator equation to the new discrete-timeplant given by (11) and (12) yields{circumflex over (x)}[k]={overscore (x)}[k]+L(i y[k]−{overscore (y)}[k]){overscore (x)}[k+1]=A _(e) x[k]+B _(e) u[k]  (14)where the variable y[k] can be pre-calculated in the stage of stateprediction according to{overscore (y)}[k+1]=C _(ed) {overscore (x)}[k+1]+D _(ed) u[k]  (15)

In Equation (14), {overscore (x)}[k] is a predicted version of the statevariable x, and {circumflex over (x)}[k] is the estimate of the stateobtained by correcting the prediction with current information.

Equation (11) shows the ideal state equation, the delay-free statefeedback law can be implemented by simply using the state estimate in(14). In this way, the time delay is automatically accommodated.

An additional advantage of this DAE is that the estimator state equationis simplified compared to the estimator in Type I. This is quite helpfulin practical implementation, where a multi-rate control strategy may beutilized.

FIGS. 4A to 5B show the impact of using the DAE examined throughcomputer simulations. These Figures use Bode plots of the servo controlsystems based upon the prior art and the invention.

Bode plots are a common way to represent the frequency response of asystem. A system's frequency response is defmed as the magnitude andphase difference between an input sinusoidal signal and the system'soutput sinusoidal signal. In the Bode plots that follow, the horizontalaxis of both upper and lower charts is in frequency, with units of Herz(Hz) displayed on a logarithmic scale.

The upper logarithmic chart of each of these Figures shows gain, and thelower logarithmic chart shows phase shift. The vertical axis of theupper charts is in decibels (dB). The vertical axis of the lower chartsis in degrees. A decibel (dB) is defined as 20*log₁₀(Magnitude).

Gain margin is defmed as the change in gain (found in the upper chart)required to cause the hard disk drive system to become unstable.

Phase margin is defmed as the phase shift required to cause the harddisk drive system to be unstable. The phase margin is the difference inphase between the frequency with a gain of 0 dB and 180°, as determinedby the Bode plot.

The dotted vertical line in the following Bode plots identifies thephase cross over frequency ƒ_(gc), which is the frequency giving a phaseof 180°. The gain margin is the difference in magnitude curve and 0 dBat the point corresponding to the phase cross over frequency.

FIG. 4A shows the Bode plots of simulating a state-space controllerreferred to as the ideal plant with standard control as found in theprior art. The state-space controller uses an ideal actuator modelfeaturing no delay as a standard controller.

In FIG. 4A, the gain margin is 5.9442 dB at 2663.6 Hz, and the phasemargin is 42.775 degrees at 1008.1 Hz.

FIG. 4B shows the Bode plots of simulating a state-space controllerreferred to as the delay plant with standard control as found in theprior art. The state-space controller uses a delay-present actuatormodel with standard controller design.

In FIG. 4B, the gain margin is 5.0633 dB at 2057.9 Hz, and the phasemargin is 33.702 degrees at 1008.1 Hz.

FIG. 5A shows the Bode plots of simulating a state-space controllerreferred to as the delay plant with delay model estimator. Thestate-space controller uses a delay-present actuator model accountingfor delay only at state-prediction stage as found in the prior art.

In FIG. 5A, the gain margin is 4.7617 dB at 2150.8 Hz, and the phasemargin is 35.965 degrees at 1006.8 Hz.

FIG. 5B shows the Bode plots of simulating a state-space controllerdesigned according to a delay-present actuator with the invention'sdelay-accommodating estimator (DAE).

In FIG. 5B, the gain margin is 5.7177 dB at 2895.4 Hz, and the phasemargin is 47.826 degrees at 933.25 Hz.

As shown in FIG. 4B compared with FIG. 4A, disregarding the computationdelay results in a significant degradation of phase margin (from 43degrees to 34 degrees).

As shown in FIG. 5A, incorporating the delay model into the predictionequations as in (3) slightly recovers the phase margin to 36 degrees, atthe cost of noticeable reduction of gain margin.

As shown in FIG. 5B, application of DAE, assuming exact knowledge of thedelay time T_(d), leads to a significant recovery of stability margins(gain margin and “first” phase margin). The DAE also reduces theopen-loop crossover frequency with the same feedback gains.

While these simulations are indicative, one skilled in the art willrecognize that exact knowledge of T_(d) is typically unavailable, andthe delay dynamics are not exactly the same as the transport model.Nonetheless, the simulation results clearly demonstrate the usefulnessof DAE design in recovering stability margins of the closed-loop system.

The invention's method was tested on an 80 GB hard disk drivemanufactured by the assignee, Samsung Electronics, Co. Ltd. Thedelay-accommodating estimator of type II was implemented and comparedwith the conventional state feedback controller. The conventionalcontroller models the computation delay as in the state prediction modelshown in the FIG. 4B.

A comparison was made for an open-loop bandwidth of 950 Hz. Thebandwidth was increased to 1.1 kHz to see how well the controllersperformed for boosted bandwidth. The resulting on-track PES statisticswere measured to compare each controller's performance in terms of TMRcapability. The adaptive feed forward controller was disabled for therejection of a particular set of repeatable run-outs, to permit a faircomparison of controllers. The experimental results are summarized inTable One. TABLE ONE Summary of experimental results 950 Hz 1100 HzCurrent DAE Current DAE f_(gc) (Hz) 959 989 1102 1084 PM (deg) 30.9 35.430.6 34.0 GM (dB) 4.8 5.0 3.9 4.5 ESF Peak 2.5 2.4 2.8 2.7 RRO 9.1 9.16.7 6.6 NRRO 10.8 9.8 8.9 8.7 PES STD 14.1 13.4 11.1 10.9

In Table One, ƒ_(gc) indicates the gain crossover frequency, also knownas servo bandwidth herein. PM is the Phase margin. GM is the gainmargin. ESF Peak is the peak amplitude of the error sensitivity function(ESF).

In Table One, RRO indicates Repeatable Run Out errors associated withtrack following, which repeat on every revolution of the disk surface.NRRO indicates Non-Repeatable Run Out errors associated with trackfollowing, which do not repeat with every disk surface revolution.

In Table One, PES STD indicates the standard deviation of the PositionError Signal.

FIG. 6A shows a comparison of the open-loop transfer functions as Bodeplots experimentally derived for the conventional controller design(labeled 300) and the DAE based controller design (labeled 310).

FIG. 6B shows a comparison of the error sensitivity functionsexperimentally derived for the conventional controller design (labeled320) and the DAE based controller design (labeled 330).

As predicted in the simulation, the use of DAE significantly recoveredboth the phase margin and the gain margin compared to the conventionalcontroller, which partially accounts for time delay. It is importantthat this recovery occurred with almost the same open-loop crossoverfrequency.

In FIG. 6A, the phase margin is shown increased near the cross overfrequency. However, in the high-frequency region, some boost of gain isobserved.

The reduction of phase margin translates to the decrease of the errorsensitivity peaking shown in FIG. 6B. This effectively attenuates theamplification ratio of disk-mode related disturbances, resulting in thereduction of standard deviation of the non repeatable PES as shown inTable One. The experimental results confirm that the DAE is practicaland useful in achieving the high-bandwidth servo systems required forhigh-TPI hard disk drives.

Experimental results using the commercial hard drive, as well as thesimulation results, show that the inventive method effectively improvesthe hard disk drive control system stability. This is done by increasingthe phase margin and the gain margin by 3-4° and 0.3 dB, respectively.

FIG. 7A shows a detail flowchart of operation 2112 of FIG. 3B furthercontrolling the voice coil actuator contained in the hard disk drive bya control variable U 2302 based upon the measured read-write headposition Ycur 2300.

In FIG. 7A, operation 2212 obtains the measured read-write head positionYcur 2300 shown in FIG. 2E. Obtaining the measured read-write headposition Ycur 2300 may include a variety of interactions involving anyor all of the channel interface 222, the embedded disk controller 1000,and resources of the servo controller 240.

In FIG. 7A, operation 2222 calculates the control variable U based uponthe measured read-write head position Ycur 2300. Operation 2222 will befirst discussed in terms of the control system equations and theirderivation, and then in terms of the invention's method in FIG. 7B.

FIG. 7B shows a detail flowchart of operation 2222 of FIG. 7Acalculating the control variable U 2302 based upon the measuredread-write head position Ycur 2300 of FIGS. 2E and 7A.

In FIG. 7B, operation 2232 performs calculating an estimated statevector Xhat 2320 based upon a predicted state vector Xbar 2330 and basedupon the difference between the measured read-write head position Ycur2300 and a predicted read-write head position Ybar 2310 of FIG. 2E.Operation 2232 is described in the first line of Equation (14), furtherusing the L 2350 of FIG. 2E.

In FIG. 7B, operation 2242 performs calculating the control variable U2302 based upon a regulator gain matrix K multiplied by the estimatedstate vector Xhat 2320 of FIG. 2E. Operation 2242 is described inEquation (4) further using the regulator gain matrix K 2340 of FIG. 2E.

In FIG. 7B, operation 2252 performs replacing the predicted state vectorXbar 2330 based upon the estimated start vector Xhat 2320 and based uponthe control variable U 2302 of FIG. 2E. Operation 2252 is described inthe second line of Equation (14), using Ae 2360 and Be 2370 of FIG. 2E.

In FIG. 7B, operation 2262 performs replacing the predicted read-writehead position Ybar 2310 based upon the predicted state vector Xbar 2330and based upon the control variable U 2302 of FIG. 2E. Operation 2262 isdescribed in equation (15) using Ced 2380 and Ded 2390 of FIG. 2E.

Note that specific embodiments of the invention may use differing valuesfor the regulator gain matrix K 2340 and the L 2350 of FIG. 2E andequations (4) and (14). Franklin contains a thorough discussion of thederivation of K and L via pole placement.

Those skilled in the art will appreciate that various adaptations andmodifications of the just-described preferred embodiments can beconfigured without departing from the scope and spirit of the invention.Therefore, it is to be understood that, within the scope of the appendedclaims, the invention may be practiced other than as specificallydescribed herein.

1. A servo controller for a hard disk drive, comprising: means forobtaining said measured read-write head position Ycur; and means forcalculating said control variable U based upon said measured read-writehead position Ycur performing the steps: calculating an estimated statevector Xhat based upon a predicted state vector Xbar and based upon thedifference between said measured read-write head position Ycur and apredicted read-write head position Ybar; calculating said controlvariable U based upon a regulator gain matrix K multiplied by saidestimated state vector Xhat; replacing said predicted state vector Xbarbased upon said estimated state vector Xhat and based upon said controlvariable U; and replacing said predicted read-write head position Ybarbased upon said predicted state vector Xbar and based upon said controlvariable U; wherein each member of a state vector collection includes aread-write head position version, a read-write head velocity version andan unknown bias force version; wherein said state vector collectionincludes said estimated state vector Xhat and said predicted statevector Xbar; wherein said hard disk drive includes a disk surfaceaccessed by a read-write head at said measured read-write head positionYcur; wherein said disk surface contains multiple physical tracks at aTrack Per Inch (TPI); and wherein said TPI is at least 80,000 tracks perinch.
 2. The servo controller of claim 1, comprising, for each step ofclaim 1, a means for implementing said corresponding step.
 3. The servocontroller of claim 1, wherein the step calculating said estimated statevector Xhat is further comprised of the step of: setting said estimatedstate vector Xhat to approximate said predicted state vector Xbar addedto an L multiplied by the difference between said measured read-writehead position Ycur and said predicted read-write head position Ybar;wherein said L relates said difference between said measured read-writehead position Ycur and said predicted read-write head position Ybar tosaid estimate state vector Xhat.
 4. The servo controller of claim 1,wherein the step replacing said predicted state vector Xbar is furthercomprises the step: setting said predicted state vector Xbar toapproximate an Ae multiplied by said estimated state vector Xhat addedto Be multiplied by said control variable U; wherein said Ae relatessaid estimated state vector XHat to said predicted state vector Xbar;and wherien said Be relates said control variable U to said predictedstate vector Xbar.
 5. The servo controller of claim 1, wherein the stepreplacing said predicted read-write head position Ybar is furthercomprised of the step of: setting said predicted read-write headposition Ybar to approximate an Ced multiplied by said predicted statevector Xbar added to a Ded multiplied by said control variable U;wherein said Ced relates said predicted state vector Xbar to saidpredicted read-write head position Ybar; and wherein said Ded relatessaid control variable U to said predicted read-write head position Ybar.6. The servo controller of claim 1, further comprising: means forcontrolling a voice coil actuator contained in said hard disk drive by acontrol variable U based upon a measured read-write head position Ycur.7. The servo controller of claim 6, wherein at least one of said meansis implemented using at least one member of the collection comprising: alow pass filter, a high pass filter, a band-pass filter, an operationalamplifier, an amplifier, a current source, a delay element, a voltagesource, a comparator, a finite state machine, a digital signalprocessor, an analog-to-digital converter, a channel interface circuit,and a digital-to-analog converter.
 8. The servo controller of claim 6,wherein the means for controlling said voice coil actuator isimplemented as a program system comprised of program steps residing in amemory accessibly coupled to a DSP; wherein said DSP controls a voicecoil directing the positioning of said voice coil actuator; wherein saidprogram system is comprised of at least one program step implementing atleast one member of the collection comprising: means for obtaining saidmeasured read-write head position Ycur; and means for calculating saidcontrol variable U based upon said measured read-write head positionYcur.
 9. The hard disk drive of claim 6, comprising: said servocontroller controlling said voice coil actuator by said control variablebased upon said measured read-write head position Ycur.
 10. A methodgenerating a control variable U for controlling a voice coil actuator ina hard disk drive, comprising the steps of: calculating an estimatedstate vector Xhat based upon a predicted state vector Xbar and basedupon the difference between a measured read-write head position Ycur anda predicted read-write head position Ybar; calculating said controlvariable U based upon a regulator gain matrix K multiplied by saidestimated state vector Xhat; replacing said predicted state vector Xbarbased upon said estimated state vector Xhat and based upon said controlvariable U; and replacing said predicted read-write head position Ybarbased upon said predicted state II vector Xbar and based upon saidcontrol variable U; wherein each member of a state vector collectionincludes a read-write head position version, a read-write head velocityversion and an unknown bias force version; wherein said state vectorcollection includes said estimated state vector Xhat and said predictedstate vector Xbar; wherein said hard disk drive includes a disk surfaceaccessed by a read-write head at said measured read-write head positionYcur; wherein said disk surface contains multiple physical tracks at aTrack Per Inch (TPI); and wherein said TPI is at least 80,000 tracks perinch.
 11. The method of claim 10, further comprising the step: obtainingsaid measured read-write head position Ycur.
 12. The method of claim 11,further comprising at least one member of the collection comprising thesteps: seeking a first track located at a first head position bydirecting said servo controller to alter said measured read-write headposition Ycur based upon said control variable U; and following saidfirst track located at said first head position by directing the servocontrol to maintain said measured read-write head position Ycur close tosaid first head position based upon said control variable U.
 13. Themethod of claim 10, wherein the step calculating said estimated statevector Xhat is further comprised of the step of: setting said estimatedstate vector Xhat to approximate said predicted state vector Xbar addedto an L multiplied by the difference between said measured read-writehead position Ycur and said predicted read-write head position Ybar;wherein said L relates said difference between said measured read-writehead position Ycur and said predicted read-write head position Ybar tosaid estimated state vector Xhat.
 14. The method of claim 10, whereinthe step replacing said predicted state vector Xbar is further comprisedof the step of: setting said predicted state vector Xbar to approximatean Ae multiplied by said estimated start vector Xhat added to Bemultiplied by said control variable U; wherein said Ae relates saidestimated state vector XHat to said predicted state vector Xbar; andwherien said Be relates said control variable U to said predicted statevector Xbar.
 15. The method of claim 10, wherein the step replacing saidpredicted read-write head position Ybar is further comprised of the stepof: setting said predicted read-write head position Ybar to approximatean Ced multiplied by said predicted state vector Xbar added to a Dedmultiplied by said control variable U; wherein said Ced relates saidpredicted state vector Xbar to said predicted read-write head positionYbar; and wherein said Ded relates said control variable U to saidpredicted read-write head position Ybar.
 16. An implementation of themethod of claim 10 further comprising for each step of claim 8, a meansfor implementing said corresponding step.
 17. The implementation ofclaim 16, wherein at least one of said means is implemented using atleast one member of the collection comprising: a low pass filter, a highpass filter, a band-pass filter, an operational amplifier, an amplifier,a current source, a delay element, a voltage source, a comparator, afinite state machine, a digital signal processor, an analog-to-digitalconverter, a channel interface circuit, and a digital-to-analogconverter.
 18. The implementation of claim 16, further comprising: adigital signal processor accessibly coupled to a memory and a programsystem comprising program steps residing in said memory; wherein saiddigital signal processor controls said voice coil directing thepositioning of said voice coil actuator; and wherein said program systemis comprised of at least one program step implementing at least onemember of the collection comprising: means for calculating saidestimated state vector Xhat; means for calculating said control variableU; means for replacing said predicted state vector Xbar; and means forreplacing said predicted read-write head position Ybar.
 19. Theimplementation of claim 18, wherein said program system furthercomprises the program steps: calculating said estimated state vectorXhat based upon said predicted state vector Xbar and based upon thedifference between said measured read-write head position Ycur and saidpredicted read-write head position Ybar; calculating said controlvariable U based upon said regulator gain matrix K multiplied by saidestimated state vector Xhat; replacing said predicted state vector Xbarbased upon said estimated state vector Xhat and based upon said controlvariable U; and replacing said predicted read-write head position Ybarbased upon said predicted state vector Xbar and based upon said controlvariable U.
 20. The control variable U as a product of the process ofclaim
 10. 21. A method of controlling said voice coil actuator in saidhard disk drive based upon said control variable U of claim 20,comprising the steps: seeking a first track located at a first headposition by directing said servo controller to alter said measuredread-write head position Ycur based upon said control variable U; andfollowing said first track located at said first head position bydirecting the servo control to maintain said measured read-write headposition Ycur close to said first head position based upon said controlvariable U.